The two-carriage service carries 270 passengers but only has capacity for 185 seated and standing, so ran nearly one-and-a-half times - or 146 per cent - full.

ScotRail is to add extra carriages to ease overcrowding. Picture: Robert Perry.

That includes 125 standing - more than three times as many as the 40 maximum who should be.

Crowding on the evening rush hour train is at its worst between Haymarket in Edinburgh and Livingston South.

Transport Scotland said new trains would not operate on the route for another two years and trains on an alternative route via Livingston North were also busy.

Second worst was the 5:01pm Glasgow Central-East Kilbride service, which operated at 135 per cent of capacity between May and September, when the winter four-carriage train is reduced to two carriages.

The worst section is between Central and Pollokshaws West, but a four-carriage train will operate year round from next summer.

The most crowded morning rush hour train was in third place - the 8:07am Neilston-Glasgow Central, at 133 per cent of capacity between Muirend and Central.

The three-carriage train will be increased to four "early" next year.

The busiest east coast train was placed fifth - the 5:53pm Edinburgh-Glenrothes, at 120 per cent of capacity.

Transport Scotland said there would be the "potential introduction" of more trains on the route from December next year.

The Office of Rail and Road (ORR) - the rail regulator - said crowded trains were low risk.

The latest figures were compiled from passenger counts over the last six months, assisting ScotRail to put available extra carriages where they were needed most.

Figures from 2015, revealed by Scotland on Sunday from a Freedom of Information request, showed the busiest train operated with twice as many passengers as seats - the 8:29am Milngavie-Edinburgh between Westerton and Glasgow Queen Street.

It said an extra 180 carriages were due to added to the network over the next two years.

Transport minister Humza Yousaf said: “We wholly appreciate busy trains can be uncomfortable and can assure passengers we are focused on delivering the value-for-money service they both want and deserve.

"We will achieve this in the near future, meanwhile this busiest trains information will help make informed journey planning choices simpler in the here and now.”

The ORR stated: "There is no legal limit on the number of passengers that can travel in any given train coach as trains differ from other modes of transport – most notably buses and aeroplanes - because of the heavy engineering design involved.

"This permits trains to operate effectively and safely even when fully loaded to maximum capacity.

"But despite being uncomfortable, and at times making passengers feel unsafe, there is no conclusive evidence linking crowding on trains with anything other than low level health and safety risks to individual passengers."

“Passengers will want to see continued investment in the rail network that sees more trains arriving on time, improved capacity and fewer cancellations.

“This is particularly required as our latest National Rail Passenger Survey showed passengers had experienced a decline of 7 per cent in overall satisfaction from the previous year, not helped by a drop in punctuality.”

TOP TEN BUSIEST SCOTRAIL TRAINS

1 1721 Edinburgh-Glasgow Central: operated at 146 per cent of total seats/standing capacity